Distance to Horizon

Last Updated on Sunday, 16 October 2011 18:04

This calculation should be taken as a guide only as it assumes the earth is a perfect sphere of diameter 7926 miles (6888 nautical miles, 12756 kilometres). It also assumes the horizon you are looking at, is the sea.

A triangle is formed with the centre of the earth C, the horizon point H and the observer O. The line of site of the Observer to the horizon is tangential to the earth’s circumference. Any angle between a tangent line to a circle and the radius of the circle is a right angle.

Using the Pythagoras theorem (The square of the hypotenuse of a right angle triangle is equal to the sum of the squares on the other two sides) we can calculate the distance from the observer to the horizon O-H. C-H is the earth's radius (r) and CO is the earth's radius (r) plus observer's height (h) above sea level.

Taking an eye height looking from the Lookout at Rhossili of 150 feet (45.72 metres), the distance to the horizon is 15.01 statute miles (13.04 nautical miles).

The distance from Rhossili Lookout to the island of Lundy is 30.5 statute miles (26.5 nautical miles), which is beyond the visible horizon.  However it can of course be seen due to its elevation of about 440 feet (134 metres).

By doing a calculation from Lundy to the same point on the horizon that we observe from the Lookout, would mean that the point at which we see Lundy is about 114 feet (35 metres) and above.

This method of calculation the distance to an object below the visible horizon is known as the ‘Rising and Dipping Range’. For example an object, such as a light, is observed to be just rising above or just dipping below the visible horizon.

For more detailed and interesting information see:

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